I'm rather sceptical about the idea that they can keep him another season and therefore qualify for the CL due to his presence in the team.
He was there last season and they failed to achieve top 4.
Given that the teams around arsenal will be improving , it's certainly not a given that they would finish top 4 this coming season, especially with Thursday night football anchoring them.
But worst of all for arsenal, if they qualify they would have to convince a player who openly says that he wants to win the CL - not just qualify only to be knocked out before the quarter finals, that they share his ambition in that respect, and given arsenal's record of failure in the tournament, that would take major leap of faith on Sanchez's part, and at 28 can he afford the risk that arsenal would suddenly change from also-rans to serious challengers in the next 3 to 4 years?